Hi Joe,
Day hikes can be done without permits on every Eastern Sierra trail, except for Whitney. All trails have a maximum daily quota for overnight hikes, and can be made with advance reservations. Here is info from Inyo National forest:
https://www.fs.usda.gov/main/inyo/passes-permits/recreationHere is tip if you haven't made a reservation in advance:
It is still possible to get an overnight permit by showing up in person at the White Mtn Ranger Station in Bishop, at 8 AM on the day before you expect to begin your hike and apply for a permit for the next day. Be early and be the first in line! There will almost always will be extra permits available. Then...at 11 AM that same day the "standby" permits for the next day are issued , at which time you can pick up yours. If you fail for show up at that time, they might give your permit to someone else. As a local resident, this is what I do every year and have never failed to get a "next day" permit. The only exception might be the Mt. Whitney trail quota, which fills very quickly.
This technique might involve an overnight stay in the Bishop area, which isn't bad. Camp at Brown's Town campground just south of Bishop or stay in a motel.
It will always be easier to get a permit for a hike that begins Monday - Thursday, than for weekend trips.
The Eastern Sierra has many beautiful trails, most of which cross over the high passes into the west side. Bishop Creek trails, Big Pine canyon, Pine Creek, etc. Just be flexible in case the trail you want has a filled quota for that particular day. The ranger station staff will be glad to help you make alternate plans.
Any questions?
